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An alternative approach to robust collocation

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Abstract

The now classical collocation method in geodesy has been derived byH. Moritz (1970; 1973) within an appropriate Mixed Linear Model. According toB. Schaffrin (1985; 1986) even a generalized form of the collocation solution can be proved to represent a combined estimation/prediction procedure of typeBLUUE (Best Linear Uniformly Unbiased Estimation) for the fixed parameters, and of type inhomBLIP (Best inhomogeneously LInear Prediction) for the random effects with not necessarily zero expectation. Moreover, “robust collocation” has been introduced by means of homBLUP (Best homogeneously Linear weakly Unbiased Prediction) for the random effects together with a suitableLUUE for the fixed parameters. Here we present anequivalence theorem which states that the robust collocation solution in theoriginal Mixed Linear Model can identically be derived as traditionalLESS (LEast Squares Solution) in amodified Mixed Linear Model without using artifacts like “pseudo-observations”. This allows us a nice interpretation of “robust collocation” as an adjustment technique in the presence of “weak prior information”.

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  1. Dept. of Geodetic Sci. & Surveying, The Ohio State University, 1958 Neil Avenue, 43210, Columbus, OH, (U.S.A.)

    Burkhard Schaffrin

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  1. Burkhard Schaffrin
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Schaffrin, B. An alternative approach to robust collocation. Bull. Geodesique 63, 395–404 (1989). https://doi.org/10.1007/BF02519637

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  • DOI: https://doi.org/10.1007/BF02519637

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